改进多项式零点的考奇半径

Q4 Mathematics
Subhasis Das
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引用次数: 0

摘要

"对于给定的复系数为 n 的多项式 p(z) =a_{n}z^{n}+a_{n-1}z^{n-1}+\cdots +a_{1}z+a_{0} ,考奇半径 r_{0} 是方程 |a_{n}| t^{n}-(|a_{n-1}|t^{n-1}+|a_{n-2}| t^{n-2}+ ... +|a_{1}| t+ |a_{0}| 的唯一正根。它指的是 p(z) 的所有零点所在的圆形区域 |z|<= r_{0} 的半径。我们的基本目标是确定最小的半径,从而使圆形区域的面积最小。在本文中,我们获得了一个改进考希半径的结果。同时,我们还得出了一个中心与 p(z) 的零点所在的原点不同的环形区域。此外,在许多情况下,我们的结果在估计多项式零点区域时给出的近似值比从许多其他著名结果中得到的近似值更好"。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An improvement of Cauchy radius for the zeros of a polynomial
"For a given polynomial p(z) =a_{n}z^{n}+a_{n-1}z^{n-1}+\cdots +a_{1}z+a_{0} of degree n with complex coefficients, the Cauchy radius r_{0} is a unique positive root of the equation |a_{n}| t^{n}-(|a_{n-1}|t^{n-1}+|a_{n-2}| t^{n-2}+ ... +|a_{1}| t+ |a_{0}|) =0. It refers to a radius of the circular region |z|<= r_{0} in which all the zeros of p(z) lie. The basic aim has been to determine the smallest radius, thereby, minimizing the area of the circular region. In this present paper, we have obtained a result which gives an improvement of the Cauchy radius. Also, we produce an annular region whose center is different from the origin in which the zeros of p(z) lie. Moreover, in many cases, our results give better approximations for estimating the region of polynomial zeros than that obtained from many other well-known results."
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来源期刊
Mathematica
Mathematica Mathematics-Mathematics (all)
CiteScore
0.30
自引率
0.00%
发文量
17
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